3V, 20mA is typical. The lamp will have a resistor inside to limit the current. As a 20mA LED is already bright
enough in the dark, I don't think they have used a more powerful one. The 5mm package shown in the photo can't handle much more anyway.
The current running through the LED is defined by input (voltage - led forward voltage) / resistor. So as long as you use a similar color (thus forward voltage) the current will be about the same.
So your average warm white LED will work just fine.
https://www.leds.de/nichia-nsdl570gs-k1-5mm-led-23lm-2700k-15037.html while expensive for a single LED, this one
should give you a really good result.
As I tried to explain already, LEDs are "defined" by their color and maximum current. Low power white LEDs should start lighting up at 3V (green at 2.4V, red at 1.8V… there are tables for that). The current is limited by the amount of heat the LED can give away at its maximum operating temperature. As most semiconductors, being cold greatly extends their lifetime. Less current works always. So you could use a 3W LED if you fancy, but it would not be any brighter.
I am in the truck towards Abkhazia right now…